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Microscopic theory of a high Tc cuprate BiSCO based on main pairing channelof electrons in CuO planes due to 40meV lateral vibrations of the apical oxygenatoms in adjacent the SrO ionic insulator layer is proposed. The separationbetween the vibrating charged atoms and the 2D electron gas creates the forwardscattering peak leading in turn to the d-wave pairing within Eliashbergformalism. The phonon mode naturally explain the kink in dispersion relationobserved by ARPES and the and effect of the O16 to O18 isotope substitution inthe normal state. To describe the pseudogap physics a single band fourfoldsymmetric Hubbard model, with the hopping parameters t' = - 0.17t and the onsite repulsion U = 6t was used. It described the Mott insulator at low doping,while at higher dopping the pseudogap physics (still strongly correlated) canbe be approximated by the symmetrized mean field model and with renormalized Uincorporating screening. The location of the transition line between thelocally antiferromagnetic pseudogap and the paramagnetic overdoped phases andsusceptibility (describing spin uctuations coupling to 2DEG) are also obtainedwithin this approximation. The superconducting d-wave gap mainly due to thephonon channel but is assisted by the spin fluctuations (15-20%). Thedependence of the gap and Tc on doping and effect of the isotope substitutionare obtained and is consistent with experiments.

Apical oxygen vibrations dominant role in d-wave cuprate superconductivity and its interplay with spin fluctuations